# Plot p.d.f. from m.g.f

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john birt on 24 Feb 2011
Knowing only the Moment Generating Function (or alternatively the Characteristic function, replacing t by it) of a distribution with five parameters, with m.g.f given by
M(t) = c(1)*t+c(2)*c(3)-c(2)*(c(3)^(1/c(4))+c(5)^2-(c(5)+t).^2).^c(4)
where
C(1) = -0.002, C(2) = 3.4654, C(3) = 28.6077, C(4) = 0.2522, C(5) = 26.4761
Can Matlab estimate and plot the Probability Density Function for the distribution?

Matt Tearle on 28 Feb 2011
Sorry, this question got a bit lost when Answers had a glitch a few days back...
I hate to state for sure that there's no function for this, but I don't know of one. (FWIW: I am not a hard-core statistician, but I have been looking pretty closely at Statistics Toolbox recently.)
Maybe there's a way using the definition, but I can't think of what it would be, off the top of my head. Hunting for it, I found this CSSM thread about it. There's a link to an article that looks promising, but you need access to Springer journals.
Sorry I couldn't be more help.
john birt on 28 Feb 2011
P.S. I would have thought Matlab would have something to do this, I am suprised!